Glossary – Guillaume Gilles

This glossary collects every mathematical symbol and term introduced across Modules 1–8, with its notation and a plain-language definition.

1 Numbers and Operations (Module 1)

Order of operations / PEMDAS (priorité des opérations): The hierarchy used to evaluate an expression: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).
Absolute value (valeur absolue), \(|a|\): The distance of a real number \(a\) from zero; \(|a| = a\) if \(a \geq 0\) and \(|a| = -a\) if \(a < 0\).
Power (puissance), \(a^{n}\): The product of \(a\) by itself \(n\) times; \(a^{0} = 1\) and \(a^{-n} = 1/a^{n}\).
Square root (racine carrée), \(\sqrt{a}\): The non-negative number \(b\) such that \(b^{2} = a\) (for \(a \geq 0\)).
Fraction (fraction), \(\dfrac{a}{b}\): A division of two real numbers with \(b \neq 0\).
Percentage (pourcentage), \(\%\): A fraction with denominator \(100\); \(t\%\) of a quantity multiplies it by \(t/100\).
Index number (indice): \(\dfrac{\text{current value}}{\text{reference value}} \times 100\); equals \(100\) at the reference level.
Proportionality (proportionnalité): Equality of two ratios; \(\dfrac{a}{b} = \dfrac{c}{x} \Rightarrow x = \dfrac{bc}{a}\).

Factoring (factorisation): Rewriting an expression as a product, using a common factor.
Expanding (développement): Rewriting a product as a sum of terms, using distributivity \(a(b + c) = ab + ac\).
Notable identity (identité remarquable): A standard algebraic equality such as \((a + b)^{2} = a^{2} + 2ab + b^{2}\) or \((a - b)(a + b) = a^{2} - b^{2}\).
First-degree equation (équation du premier degré), \(ax + b = 0\): An equation whose solution is \(x = -b/a\) when \(a \neq 0\).

Cartesian plane (plan cartésien): A plane with an orthonormal coordinate system of two perpendicular axes.
Slope (pente / coefficient directeur), \(m\): The rate of change of \(y\) with respect to \(x\) in a line \(y = mx + p\).
\(y\)-intercept (ordonnée à l’origine), \(p\): The value of \(y\) where the line crosses the \(y\)-axis (\(x = 0\)).
System of equations (système d’équations): Several equations to be satisfied simultaneously; the graphical solution is the intersection point of the lines.
Inequality (inéquation): A relation with \(<, \leq, >, \geq\); multiplying/dividing by a negative number reverses the direction.

Numerical sequence (suite numérique), \(u_n\): An ordered list of numbers indexed by the whole numbers; \(u_0\) is the first term.
Arithmetic sequence (suite arithmétique): \(u_{n+1} = u_n + r\); explicit form \(u_n = u_0 + nr\), with common difference \(r\).
Common difference (raison arithmétique), \(r\): The constant added at each step of an arithmetic sequence.
Geometric sequence (suite géométrique): \(u_{n+1} = u_n \times q\); explicit form \(u_n = u_0 q^{n}\), with common ratio \(q\).
Common ratio (raison géométrique), \(q\): The constant factor multiplied at each step of a geometric sequence.

Simple interest (intérêts simples): Interest computed only on the initial capital; \(C_n = C_0(1 + in)\) (arithmetic).
Compound interest (intérêts composés): Interest that itself earns interest; \(C_n = C_0(1 + i)^{n}\) (geometric).
Interest rate (taux d’intérêt), \(i\): The rate applied per period; simple rates convert proportionally, compound rates via \((1 + i_m)^{12} - 1\).
Average placement rate (taux moyen de placement): The single rate giving the same final capital as several combined investments.

Function (fonction), \(f : x \mapsto f(x)\): A process associating to each number a unique image.
Domain of definition (domaine de définition), \(D_f\): The set of \(x\) for which \(f(x)\) can be computed.
Sense of variation (sens de variation): Whether a function is increasing or decreasing on an interval.
Parity (parité): Even if \(f(-x) = f(x)\); odd if \(f(-x) = -f(x)\).
Discriminant (discriminant), \(\Delta = b^{2} - 4ac\): Determines the number of real roots of \(ax^{2} + bx + c = 0\).
Logarithm / exponential (logarithme / exponentielle), \(\ln x,\; e^{x}\): Inverse functions; \(\ln(ab) = \ln a + \ln b\) and \(e^{a+b} = e^{a}e^{b}\).

Average rate of change (taux de variation moyen), \(\tau\): \(\dfrac{f(x_2) - f(x_1)}{x_2 - x_1}\); the slope of the secant line.
Derivative (dérivée), \(f'(x)\): The instantaneous rate of change; the slope of the tangent line; \((x^{n})' = n x^{n-1}\).
Optimization (optimisation): Finding a maximum or minimum; for \(ax^{2} + bx + c\) the extremum is at \(x = -\dfrac{b}{2a}\) (max if \(a < 0\), min if \(a > 0\)).